Yes you can sue the police department however they enjoy qualified immunity.
It is a high burden to overcome.
The ultimate issue will be whether or not there existed probable cause for your arrest.
The legal standing and the merits of a possible civil action against the police department must be evaluated by a very good local attorney in Florida who will examine the viability of your case in person. Without meeting you it is impossible to state whether you have a case based on one short Avvo paragraph.
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Set up consultations with a few attorneys in your area. No one can say if you have a case or not without knowing all of the facts.
R. Jason de Groot, Esq., 386-337-8239